Fractional Brownian Motion

Fractional Brownian motion (fBm) is a stochastic process extending Brownian motion to model systems exhibiting long-range dependence and self-similarity, characterized by a Hurst exponent reflecting the strength of these correlations. Current research focuses on accurately estimating the Hurst exponent using deep learning architectures like convolutional neural networks and LSTMs, surpassing traditional statistical methods in efficiency and accuracy for certain processes. These advancements are impacting diverse fields, including finance, image inpainting, topic modeling, and even brain tissue segmentation, by enabling more realistic modeling of complex temporal dynamics and improved data analysis.